Summary:

The Spectral Angle Mapper is a tool used in remote sensing and image processing to classify and identify materials based on their spectral signatures.
A spectral vector is an n_B-dimensional vector, where each component of the vector is its reflectance in the corresponding band. By calculating the angle between two spectral vectors, we can determine the similarity of the materials they represent.
This classification is not affected by changes in illumination that affect all bands in a similar way, as it only considers the angle and not the magnitude of the spectral vector.
In this project, the concept of spectral angle mapping classification is generalized from 2D to higher dimensional vectors. It uses the np.linalg.norm method to calculate the length of the spectral signature and np.dot method to calculate their dot products.
For vectors $\stackrel{^<!--\; ^\; -->}{\mathbf{\text{p}}}and\stackrel{^<!--\; ^\; -->}{\mathbf{\text{q}}}$their dot product is given by the formula,
$$\cos <!--\; \; -->\theta ={\displaystyle \frac{\stackrel{^<!--\; ^\; -->}{\mathbf{\text{p}}}\cdot <!--\; \cdot \; -->\stackrel{^<!--\; ^\; -->}{\mathbf{\text{q}}}}{||\stackrel{^<!--\; ^\; -->}{\mathbf{\text{p}}}||||\stackrel{^<!--\; ^\; -->}{\mathbf{\text{q}}}||}}$$ Where $||\stackrel{^<!--\; ^\; -->}{\mathbf{\text{p}}}||$ and $||\stackrel{^<!--\; ^\; -->}{\mathbf{\text{p}}}||$ are the lengths of vectors $\stackrel{^<!--\; ^\; -->}{\mathbf{\text{p}}}and\stackrel{^<!--\; ^\; -->}{\mathbf{\text{q}}}$
, respectively, and θ is the angle between them.
By implementing the Spectral Angle Mapper, we can accurately classify and identify materials in remote sensing and image processing applications.